The prior art discloses elastic polyester resins made of certain ordered block copolymers as disclosed in U.S. Pat. Nos. 3,023,192 and 3,954,689. Also, elastomeric properties are obtained in copolyesters having branched chain compounds in their structure as illustrated in U.S. Pat. No. 4,013,624 and esters that contain side chains as shown in U.S. Pat. No. 3,890,279. The present elastomeric copolyesters are random copolymers and different from the prior art materials by being straight chain polymers that contain significant amounts of polyalkylene groups within the polymer chain. These materials crystallize rapidly into opaque solids that are tough and elastic. They have a wide range of service temperatures and can be extruded into rods, tubes, hose, filaments and films and they can be injection molded or rotational molded into tires and parts having industrial uses.